I still have trouble with this two symbol, ∀ and ∃.?

Question

1. ∀x∃y, x^2 + 1 = y^2

2. ∃y∀x, x^2 + 1 = y^2

3. ∀y∃x x^2 + 1 = y^2

I know what the symbols mean but when they are together determining x and y, it becomes very confusing for me. Can someone give a detailed explantation to me? Thanks!

Answer 1

∀ means "for all"
∃ means "there exists"

so
∀x∃y, x^2 + 1 = y^2
means, for all x, there exists a y such that x^2 + 1 = y^2

Answer 2

Arts and Entertainment Network
Upside down easel
Table laid sideways
Traingle open
Art and Entertainment are two times arrowed up by 2 people which equals three plus 1, and yes upstairs by no. 2,
so basically peace sign equals sideways table.